Heat a grill to medium-high.
Roll and stretch the dough into a 15-inch round on a sheet of parchment paper. Brush the dough with the oil. Flip the dough onto the hot grill grate, peel off the parchment, and cover the grill. Grill until the bottom of the dough has browned and developed grill marks, about 2 minutes.
Flip the dough over and reduce the heat to medium. Spread the sauce all over the dough, then top with the mozzarella and zucchini. Cover and grill until the cheese melts and the bottom of the crust has browned, about 4 minutes.
Transfer the pizza to a large cutting board. Top with the prosciutto, pecorino, and basil. Cut into slices and serve immediately.
You can swap any summer squash for the zucchini and Classico® pizza sauce for the Tomato Basil sauce.